A057891 In base 2, neither a palindrome nor becomes a palindrome if trailing 0's are omitted.

11, 13, 19, 22, 23, 25, 26, 29, 35, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 57, 58, 59, 61, 67, 69, 70, 71, 74, 75, 76, 77, 78, 79, 81, 82, 83, 86, 87, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 105, 106, 109, 110, 111, 113, 114, 115, 116, 117, 118

Offset: 1

Author

Marc LeBrun, Sep 25 2000

Keywords

• easy
• nonn
• base

Comments

These could be called "asymmetric bit strings".

Fixed pairs of A057889, complement of A057890.

If these numbers are converted to their binary polynomial, one of the roots of that polynomial will have absolute values other than 1 or 0. For example 11 = 2^3 + 2^1 + 2^0, the absolute values of the roots of x^3 + x + 1 are 0.682328... and 1.21061... which are not 1 or 0, so 11 is in the sequence. The first number with this property which is not a term is A057890(53) = 107. - Benedict W. J. Irwin, Sep 07 2017 and Andrey Zabolotskiy, Oct 13 2017

Examples

			11 is included because 1011 is asymmetrical, but 12 is not because 001100 is a palindrome.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061917, A006995. Complement of A057890.

Cf. A030101, A000265, A006519, A057889.

Programs

Haskell

a057891 n = a057891_list !! (n-1)
a057891_list = filter ((== 0) . a178225 . a000265) [1..]
-- Reinhard Zumkeller, Oct 21 2011

Formula

A030101(A030101(n)) != A030101(n). - David Wilson, Jun 09 2009, Jun 18 2009

A178225(A000265(a(n))) = 0. - Reinhard Zumkeller, Oct 21 2011

Extensions

Edited by N. J. A. Sloane, Jun 09 2009 at the suggestion of Ray Chandler

A-numbers in formula corrected by R. J. Mathar, Jun 18 2009